Two basic approaches have been employed for the longitudinal control of vehicles in automated guideway transit systems. The approach, termed "vehicle following", allows communication between successive vehicles so that the motion of a given vehicle is controlled in accordance with the motion of a preceding vehicle. This approach contrasts with "point-following" which assigns a vehicle to a cell (or slot), the cells being propagated along the guideway network at predetermined velocities and spacings. In point-following, propulsion commands are generated to maintain the vehicle's location within the assigned cells.
Several investigators have studied the feasibility of the vehicle following approach by using a linear, time-invariant regulator to control perturbations from a nominal operating condition. Levine and Athans in "On the Optimal Error Regulation of a String of Moving Vehicles", IEEE Transactions, Vol. AC-11, No. 3, July 1966, use a linear optimal regulator to design a system where each vehicle generates propulsion commands based on information from all other vehicles in a string. In another article, "On the Optimal and Suboptimal Position and Velocity Control of a String of High Speed Moving Trains", M.I.T. Electronic Systems Laboratory, Report PB 173640, November 1966, Athans, et al reduce the complexity of this technique by applying the optimization procedure of Levine and Athans to smaller overlapping strings. Finally, Cunningham and Hinman in "An Approach to Velocity Spacing Regulation and the Merging Problem in Automated Transportation", Joint Transportation Engineering Conference, Chicago, Ill., October 1970, reduce the scheme to one in which vehicle control is based only on vehicle state and the state of the immediately preceding vehicle. This strategy is pursued by Brown in "Design of Car-Following Type Control Systems with Finite Bandwidth Plants", Proceedings of the Seventh Annual Princeton Conference on Information Sciences and Systems, March 1973 while Fenton in "Fundamental Studies in the Automatic Longitudinal Control of Vehicle", DOT-TST-76-79, July 1975, deals with the design and testing of hardware systems. In "Vehicle-Follower Longitudinal Control for Automated Transit Vehicles", ASME Journal of Dynamic Systems, Measurement, and Control, Volume 99, Number 4, December 1977, Caudill and Garrard Study the effects of spacing policy and system nonlinearities upon string stability for vehicles operating under vehicle following.
The above studies of vehicle following have focused on the regulation of vehicle speeds and spacings during perturbations about normal values. It has been shown that suitable control can be obtained using properly designed, constant-gain linear regulator laws. However, in general, a control capability must exist to perform transient manuevers such as overtaking a slower moving vehicle, switching from an open-loop velocity command mode to the regulation mode, merging vehicles both on the main line and from stations, and generating gaps in vehicle flows during such merging operations. This was first recognized by Stupp et al in "Vehicle-Follower Control with Variable-Gains for Short Headway Automated Guideway Transit Systems", ASME Journal of Dynamic Systems, Measurement, and Control, Volume 99, September 1977.
In Stupp where it was shown that at time headways of less than approximately five seconds, a fundamental kinematic constraint arises which creates bounds on vehicle motion. This constraint dictates a minimum allowable spacing between vehicles which is a function of trailing vehicle state, preceding vehicle state, and the future maneuver capability of each vehicle. As a result, the bandwidth requirement for the closed loop regulator at short headways is inconsistent with the large initial values of vehicle motion, i.e., the system response to these initial conditions typically leads to violation of comfort criteria and the kinematically required spacing.